%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET025-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 05:22:47 EDT 2022

% Result   : Unsatisfiable 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   7 unt;   0 nHn;   9 RR)
%            Number of literals    :   11 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ little_set(ordered_pair(a,b)),
    file('SET025-4.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ member(u,v)
    | little_set(u) ),
    file('SET025-4.p',unknown),
    [] ).

cnf(9,axiom,
    little_set(non_ordered_pair(u,v)),
    file('SET025-4.p',unknown),
    [] ).

cnf(11,axiom,
    equal(non_ordered_pair(singleton_set(u),non_ordered_pair(u,v)),ordered_pair(u,v)),
    file('SET025-4.p',unknown),
    [] ).

cnf(60,axiom,
    ( ~ little_set(u)
    | member(u,universal_set) ),
    file('SET025-4.p',unknown),
    [] ).

cnf(144,plain,
    ~ member(ordered_pair(a,b),u),
    inference(res,[status(thm),theory(equality)],[2,1]),
    [iquote('0:Res:2.1,1.0')] ).

cnf(146,plain,
    ~ little_set(ordered_pair(a,b)),
    inference(res,[status(thm),theory(equality)],[60,144]),
    [iquote('0:Res:60.1,144.0')] ).

cnf(466,plain,
    little_set(ordered_pair(u,v)),
    inference(spr,[status(thm),theory(equality)],[11,9]),
    [iquote('0:SpR:11.0,9.0')] ).

cnf(470,plain,
    $false,
    inference(unc,[status(thm)],[466,146]),
    [iquote('0:UnC:466.0,146.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SET025-4 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n012.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul 11 00:18:58 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.49  
% 0.20/0.49  SPASS V 3.9 
% 0.20/0.49  SPASS beiseite: Proof found.
% 0.20/0.49  % SZS status Theorem
% 0.20/0.49  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.49  SPASS derived 295 clauses, backtracked 8 clauses, performed 3 splits and kept 390 clauses.
% 0.20/0.49  SPASS allocated 76218 KBytes.
% 0.20/0.49  SPASS spent	0:00:00.14 on the problem.
% 0.20/0.49  		0:00:00.04 for the input.
% 0.20/0.49  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.49  		0:00:00.01 for inferences.
% 0.20/0.49  		0:00:00.00 for the backtracking.
% 0.20/0.49  		0:00:00.06 for the reduction.
% 0.20/0.49  
% 0.20/0.49  
% 0.20/0.49  Here is a proof with depth 2, length 9 :
% 0.20/0.49  % SZS output start Refutation
% See solution above
% 0.20/0.49  Formulae used in the proof : prove_ordered_pairs_are_small a2 non_ordered_pair4 ordered_pair universal_set
% 0.20/0.49  
%------------------------------------------------------------------------------